Observed Flow Reversals and Measured-Predicted Nusselt Numbers for Natural Convection in a One-Sided Heated Vertical Channel

1984 ◽  
Vol 106 (2) ◽  
pp. 325-332 ◽  
Author(s):  
E. M. Sparrow ◽  
G. M. Chrysler ◽  
L. F. Azevedo
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Vertical Channel ◽  
Threshold Value ◽  
Channel Length ◽  
Heated Wall ◽  
Number Range ◽  
Channel One ◽  
Recirculating Flow ◽  
Nusselt Numbers

A three-part study encompassing both experiment and analysis has been performed for natural convection in an open-ended vertical channel. One of the principal walls of the channel—the heated wall—was maintained at a uniform temperature, while the other principal wall was unheated. The experiments, which included flow visualization and Nusselt number measurements, were carried out with water in the channel and in the ambient which surrounds the channel. At Rayleigh numbers which exceeded a threshold value, the visualization revealed a pocket of recirculating flow situated adjacent to the unheated wall in the upper part of the channel. The recirculation was fed by fluid drawn into the top of the channel, adjacent to the unheated wall. Average Nusselt numbers for the heated wall were measured over a three orders of magnitude range of a single correlating parameter, which includes the Rayleigh number and the ratio of the channel length to the interwall spacing. The Nusselt numbers were found to be unaffected by the presence of the recirculation zone. Numerical solutions obtained via a parabolic finite difference scheme yielded Nusselt numbers in good agreement with those of experiment. The numerical results covered the Prandtl number range from 0.7 to 10.

Natural Convection From a Horizontal Cylinder—Turbulent Regime

1982 ◽  
Vol 104 (2) ◽  
pp. 228-235 ◽  
Author(s):  
B. Farouk ◽  
S. I. Gu¨c¸eri
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Equation Model ◽  
Turbulence Structure ◽  
Turbulent Regime ◽  
Closed Set ◽  
Number Range ◽  
Turbulent Natural Convection ◽  
Nusselt Numbers

A two-equation model has been adopted in obtaining numerical solutions of turbulent natural convection from an isothermal horizontal circular cylinder. The k-ε model employed in this study characterizes turbulence through the kinetic energy and its volumetric rate of dissipation. The transport equations for these two variables, along with those for time-averaged stream function, vorticity, and temperature, form a closed set of five coupled partial differential equations. These equations are solved for the entire flow domain, without boundary layer approximations. Buoyancy effects on the turbulence structure are also accounted for. Results are presented for a Rayleigh number range of 5×107 to 1010 and the average Nusselt numbers are compared with existing correlations and limited available experimental data.

Reversed Flow Structure and Heat Transfer Measurements for Buoyancy-Assisted Convection in a Heated Vertical Duct

1992 ◽  
Vol 114 (4) ◽  
pp. 928-935 ◽  
Author(s):  
C. Gau ◽  
K. A. Yih ◽  
W. Aung
Keyword(s):  
Heat Transfer ◽  
Vertical Channel ◽  
Flow Region ◽  
Threshold Value ◽  
Convection Flow ◽  
Parallel Plates ◽  
Reversed Flow ◽  
Recirculating Flow ◽  
Buoyancy Parameter ◽  
Complex Phenomena

Buoyancy-assisted convection flow and heat transfer processes in a heated vertical channel are studied experimentally for situations where the buoyancy parameter Gr/Re2 is relatively large. The channel wall is made of two parallel plates, with one wall heated uniformly and the opposite wall insulated. A uniform air flow is made to enter the channel from the bottom. The reversed flow is visualized, which occurs initially near the channel exit for the case when Gr/Re2 is greater than a threshold value. The cold reversed flow enters the channel from the outside and forms a V-shaped recirculating flow region in the downstream part of the duct. This region gradually propagates upstream as the buoyancy parameter Gr/Re2 increases. The counterflow motion, leading to mixing between the heated buoyant fluid and the V-shaped recirculation, is shown to be highly unstable and characterized by generation of eddies and vortices when the value of Gr/Re2 is large. An increase in Re has the effect of pushing the reversed flow downstream and making the recirculating region wider. Temperature fluctuations are measured to provide insight into the complex phenomena being studied. The penetration depth of the reversed flow is measured and compared with prediction based on a simple model. Local and average Nusselt numbers are also measured and presented.

Analysis of the Convergent Channel as an Extensional Rheometer

1999 ◽  
Author(s):  
P. R. Souza Mendes ◽  
R. L. Thompson ◽  
A. O. Nieckele
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Numerical Solutions ◽  
Mechanical Energy ◽  
Flow Characteristics ◽  
Channel Length ◽  
Geometrical Parameters ◽  
Inlet Section ◽  
Convergent Channel ◽  
Number Range

Abstract An important aspect while designing an “R2 z = constant” convergent channel as an extensional rheometer is the appropriate choice of the geometrical parameters and of the Reynolds number range of operation. The higher is the Reynolds number value, the thinner will be the boundary layer where the undesirable no-slip effect is confined, as discussed in the literature. However, if the Reynolds number, Re, is too large, then shear-related pressure losses become important, which is also undesirable in rheometry. Therefore, one design task is to find a range of Re within which the boundary layer is thin enough, and the velocity field in most of the domain is reasonably close to the desired kinematics. In this work we obtained numerical solutions for the flow of Newtonian and viscoelastic fluids through a convergent channel, for representative ranges of Re, dimensionless channel length, L, and dimensionless axial coordinate of inlet section, z0. For all cases, we determined fields of flow type, where regions of shear and of extension can be visualized. Among other findings, it is shown that, depending on the geometrical and flow characteristics, most of the mechanical energy dissipated can be due to shear effects, so that the extensional viscosity cannot be determined via pressure drop measurements.

High Rayleigh Number Laminar Natural Convection in an Asymmetrically Heated Vertical Channel

1989 ◽  
Vol 111 (3) ◽  
pp. 649-656 ◽  
Author(s):  
B. W. Webb ◽  
D. P. Hill
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Channel ◽  
Local Heat Transfer ◽  
Heated Wall ◽  
Uniform Heat Flux ◽  
Parallel Plates ◽  
Heating Rates ◽  
Wide Range

Experiments have been performed to determine local heat transfer data for the natural convective flow of air between vertical parallel plates heated asymmetrically. A uniform heat flux was imposed along one heated wall, with the opposing wall of the channel being thermally insulated. Local temperature data along both walls were collected for a wide range of heating rates and channel wall spacings corresponding to the high modified Rayleigh number natural convection regime. Laminar flow prevailed in all experiments. Correlations are presented for the local Nusselt number as a function of local Grashof number along the channel. The dependence of both average Nusselt number and the maximum heated wall temperature on the modified Rayleigh number is also explored. Results are compared to previous analytical and experimental work with good agreement.

Experimental Investigation of Natural Convection in an Asymmetrically Heated Vertical Channel with an Asymmetric Chimney

2005 ◽  
Vol 127 (8) ◽  
pp. 888-896 ◽  
Author(s):  
Oronzio Manca ◽  
Marilena Musto ◽  
Vincenzo Naso
Keyword(s):  
Heat Flux ◽  
Experimental Investigation ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Vertical Channel ◽  
Expansion Ratio ◽  
Uniform Heat Flux ◽  
Geometrical Parameters ◽  
Nusselt Numbers ◽  
Lower Maximum

An experimental investigation on air natural convection, in a vertical channel asymmetrically heated at uniform heat flux, with downstream unheated parallel extensions, is carried out. One extension is coplanar to the unheated channel wall and the distance between the extensions is equal to or greater than the channel gap (geometrically asymmetric chimney). Experiments are performed with different values of the wall heat flux, aspect ratio (Lh∕b), extension ratio (L∕Lh) and expansion ratio (B∕b). For the largest value of the aspect ratio (Lh∕b=10), the adiabatic extensions improve the thermal performance in terms of lower maximum wall temperature of the channel. Optimal configurations of the system with asymmetrical chimney are detected. Flow visualization shows a cold inflow in the channel-chimney system that penetrates down below the channel exit section. Maximum wall temperatures and channel Nusselt numbers are correlated to the channel Rayleigh number, Ra*, and to the geometrical parameters, in the ranges 3.0×102⩽Ra*B∕b⩽1.0105, 1.0⩽B∕b⩽3.0 and 1.0⩽L∕Lh⩽4.0 with Lh∕b=5.0 and 10.0.

Natural Convection in a Stably Heated Corner Filled With Porous Medium

1985 ◽  
Vol 107 (2) ◽  
pp. 293-298 ◽  
Author(s):  
S. Kimura ◽  
A. Bejan
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Single Cell ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Number Range ◽  
Corner Flow ◽  
Horizontal Wall

This is a study of the single-cell natural convection pattern that occurs in a “stably heated” corner in a fluid-saturated porous medium, i.e., in the corner formed between a cold horizontal wall and a hot vertical wall situated above the horizontal wall, or in the corner between a hot horizontal wall and a cold vertical wall situated below the horizontal wall. Numerical simulations show that this type of corner flow is present in porous media heated from the side when a stabilizing vertical temperature gradient is imposed in order to suppress the side-driven convection. Based on numerical solutions and on scale analysis, it is shown that the single cell corner flow becomes increasingly more localized as the Rayleigh number increases. At the same time, the mass flow rate engaged in natural circulation and the conduction-referenced Nusselt number increase. Numerical results for the flow and temperature fields and for the net heat transfer rate are reported in the Darcy-Rayleigh number range 10–6000.

scholarly journals An Analytical Model for Natural Convection in a Rectangular Enclosure with Differentially Heated Vertical Walls

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3220
Author(s):  
Alberto Fichera ◽  
Manuel Marcoux ◽  
Arturo Pagano ◽  
Rosaria Volpe
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Analytical Model ◽  
Numerical Solutions ◽  
Heat Fluxes ◽  
Rectangular Enclosure ◽  
Nusselt Numbers ◽  
Pressure Fields ◽  
Vertical Walls ◽  
Temperature And Velocity Fields

This paper proposes an analytical model for natural convection in a closed rectangular enclosure filled by a fluid, with imposed heat fluxes at the vertical walls and adiabatic horizontal walls. The analytical model offers a simplified, but easy to handle, description of the temperature and velocity fields. The predicted temperature, velocity, and pressure fields are shown to be in agreement with those obtained from a reliable numerical model. The Nusselt numbers for both the analytical and numerical solutions are then calculated and compared, varying both the aspect ratio of the enclosure and the Rayleigh number. Based on the comparisons, it is possible to assess the dependence of the reliability of the analytical model on the aspect ratio of the enclosure, showing that the prediction error rapidly decreases with the increase of the enclosure slenderness.

Thermal Drag and Critical Heat Flux for Natural Convection of Air in Vertical Parallel Plates

1993 ◽  
Vol 115 (1) ◽  
pp. 124-129 ◽  
Author(s):  
Zeng-Yuan Guo ◽  
Xiao-Bo Wu
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Critical Heat Flux ◽  
Numerical Solutions ◽  
Vertical Channel ◽  
Wall Heat Flux ◽  
Uniform Heat Flux ◽  
Parallel Plates ◽  
Constant Property ◽  
Flux Boundary Condition

Variable property effects on vertical channel natural convection in air are studied systematically. Numerical solutions of the governing equations show that both the mass flow rate and heat transfer in the channel are not only lower than the constant property results, but also show a nonmonotonic variation with increasing wall temperature or wall heat flux. This phenomenon, which seemingly conflicts with the conventional knowledge, has also been identified by experiments. For a vertical channel with a uniform heat flux boundary condition, the wall may experience a sharp rise in temperature up to damage of the channel if the wall heat flux is greater than the critical heat flux. This implies that the crisis phenomenon (or burnout) may occur in channel natural convection in gas as well as in the boiling process.

Natural Convection in a Rectangular Porous Cavity With Constant Heat Flux on One Vertical Wall

1984 ◽  
Vol 106 (1) ◽  
pp. 152-157 ◽  
Author(s):  
V. Prasad ◽  
F. A. Kulacki
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Local Heat ◽  
Constant Heat Flux ◽  
Heated Wall ◽  
Width Ratio ◽  
Constant Heat ◽  
Nusselt Numbers

Numerical solutions for two-dimensional, steady, free convection are presented for a rectangular cavity with constant heat flux on one vertical wall, the other vertical wall being isothermally cooled. The horizontal walls are insulated. Results are presented in terms of streamlines and isotherms, local and average Nusselt numbers at the heated wall, and the local heat flux at the cooled wall. Flow patterns are observed to be quite different from those in the case of a cavity with both vertical walls at constant temperatures. Specifically, symmetry in the flow field is absent and any increase in applied heat flux is not accompanied by linearly proportional increase in the temperature on the heated wall. Also, for low Prandtl number, the heat transfer rate based upon the mean temperature difference is higher as compared to experimental results for the isothermal case. Heat transfer results, further, indicate that the average Nusselt number is correlated by a relation of the form Nu = constant Ra*mAn, where Ra* is the Rayleigh number and A the height-to-width ratio of the cavity.

scholarly journals Experimental investigation of natural convection in an enclosure with partial partitions at different angles

2014 ◽  
Vol 18 (4) ◽  
pp. 1133-1144 ◽  
Author(s):  
Osameh Ghazian ◽  
Hossein Rezvantalab ◽  
Mehdi Ashjaee
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Wood Fiber ◽  
Convection Heat Transfer ◽  
Heated Wall ◽  
Isolated Cells ◽  
Nusselt Numbers ◽  
Vertical Walls ◽  
Rayleigh Numbers ◽  
Partial Partitions

Natural convection heat transfer in a partially partitioned enclosure has been investigated experimentally using Mach-Zehnder Interferometry technique. The top and bottom of the enclosure are insulated while one of the vertical walls is heated isothermally. The partitions are made of wood fiber and are attached to the heated wall with angles changing from 30? to 150? in different experiments. The length of each partition is equal to the width of the enclosure, therefore dividing the enclosure to isolated cells only at 90?. At other angles the cells are interconnected near the cold wall. Rayleigh number based on the enclosure width is changed from 3500 to 32000. Results for the local and the average Nusselt numbers at the heated wall of the enclosure are presented and discussed for various partition angles and Rayleigh numbers. It is found that, at each Rayleigh number, there exists an optimum inclination angle which minimizes the average Nusselt number.

Sign in / Sign up

Export Citation Format

Share Document